Introduction

The electric conductivity of an insulating polymer can beincreased when it is compounded with conductive llerssuch as copper powders, silver powders, and carbonblack powders. The improvement obtained with metalpowders is insignicant because the metal particles aretoo large to create sucient contacts. Among all theavailable llers, carbon black (CB) is the most eectiveone [1, 2, 3, 4, 5, 6, 7, 8, 9].

Carbon black is formed by combusting heavy oilsin a furnace. The carbon condenses in droplets, calledprime particles. The prime particles coalesce into

aggregates. Aggregates composed of few prime parti-cles compactly fuse to form low-structure blacks; thoseof many prime particles can generate high-structureblacks with considerable branches. For a given massof CB aggregates, a high-structure black usually pre-sents a greater surface area for electron conductionthan does a low-structure black. However, once thestructure is built, typical hydrodynamic shear forcescannot deform it. This paper uses the term uy todenote high-structure CB aggregates that exhibit goodconductivity. In certain situations, aggregates cancluster into large groups, bound by Van der Waalsforces, called agglomerates. Agglomerates are typically

ORIGINAL CONTRIBUTIONColloid Polym Sci (2002) 280: 11101115DOI 10.1007/s00396-002-0718-8

S.-P. RweiF.-H. KuK.-C. Cheng

Dispersion of carbon black in a continuousphase: Electrical, rheological,and morphological studies

Received: 17 October 2001Revised: 11 April 2002Accepted: 15 April 2002Published online: 20 June 2002 Springer-Verlag 2002

S.-P. Rwei (&) F.-H. KuInstitute of Organic and PolymericMaterials, National Taipei Universityof Technology, Taipei, Taiwan, R.O.C.E-mail: f10714@ntut.edu.twTel.: +8862-27712171 ext. 2432Fax: +8862-27317174

K.-C. ChengDepartment of Chemical Engineering,National Taipei University of Technology,Taipei, Taiwan, R.O.C.

Abstract This work investigates thedispersion of carbon black (CB)aggregates into various polymericmatrices to increase electricconductivity. The eect of matrixviscosity on CB morphology and,consequently, on the blend conduc-tivity was thoroughly addressed.The electric conductivity increasesfrom 109 to 104 when less than3% CB aggregates were dispersedinto the PDMS liquid of variousviscosities. The CB threshold load-ing was found to increase from 1%to 3% as the viscosity rose from10 cp to 60 000 cp. This ndingshows that an ideal loading withCB aggregates is far below that(generally 15%) of a typical pellet-ized CB loading. Moreover, themicroscope and RV tests reveal thatCB aggregates diuse and form anagglomerate-network when the

conductivity threshold is reachedin a low-viscosity matrix. However,a CB aggregate-network wasobserved when the threshold valuewas attained in a high-viscositymatrix. These two mechanisms canbe distinguished at approximately1000 cp. Finally, experimentalobservation shows that the increaseof viscosity during curing does notinuence the conductivity of thecomposite while the CB aggregatesdispersed in a thermoset matrix.The minimum viscosity duringcuring, however, was found to becritical to CB dispersion morphol-ogy and, consequently, to ultimateelectric conductivity.

Keywords Electric conductivity Matrix viscosity Aggregate-network Agglomerate-network Conductivity threshold

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10100 lm in size and can be broken by hydrody-namic forces.

Compounding plastic with conductive uy CB canincrease the conductivity by ve to six orders of mag-nitude. Such an application was commercialized overtwenty years ago and has been widely employed in an-tistatic or ltration elds. Conductive blends can beprepared in several ways. The most popular method is tocompound CB pellets (about 12 mm in size) into apolymeric matrix, using a banbury mixer or twin-screwextruder [10, 11, 12, 13, 14, 15, 16, 17, 18]. However,most related studies have focused on improving bulkproperties, such as electric conductivity or mechanicalproperties of the blends, as the CB agglomerates weredispersed into the polymeric matrix by intensive shear-ing. Scientists generally agree that for a given weight ofcarbon black, ner agglomerates enable more particlesto be evenly distributed in a xed volume of plastic.Thus, smaller interparticular distances can be achievedand, consequently, electrons can be transferred fromparticle to particle throughout the matrix. Accordingly,a system that includes all its CB particles in uy form,with the size of aggregate, may be in its optimal condi-tion for electron conductivity. However, the impact ofmatrix properties, such as viscosity and the degree ofcrosslinking, on the aggregate dispersion and, conse-quently, on the blends conductivity have not been ex-tensively examined.

This work focuses on the dispersion of conductiveuy CB in PDMS (poly-dimethyl siloxane) liquid ofvarious viscosities. The dispersion morphology was re-lated to the electric conductivity of the blend. The eectsof crosslinking of the polymeric matrix on the CB dis-persion and on the conductivity of the thermoset com-posite were also examined. This study aims to yieldfurther insight into the relationship between CB dis-persion and the resulting conductivity in a xed, ther-moplastic system over a range of viscosities and athermoset system. Results in this study can be applied toassess the ideal compounding ratio of CB aggregates in agiven polymeric system. Moreover, the discrepancy be-tween the feeding ratio of an ideal and that of a realsystem, into which CB is compounded, is reasonablyexplained.

Experimental procedures

Fluy carbon black (CB) was used as a conductive ller: VulcanXC72, supplied by Cabot, had aggregate density of 1.8 g/cm3, asurface area of 254 m2/g (N2), and a plasticizer absorption value,DBP (dibutyl phthalate), of 188 ml/100 g. Various grades ofpoly(dimethyl siloxane) (PDMS, 99.6% purity) from Dow Cornig,with viscosities from 10 cp to 60 000 cp were used as suspendingmedia for the uy CB powders. Uncrosslinked silicon rubber(RTV-573, Rhodorsil) with a crosslinking agent (60R, Rhodorsil)was used as another CB suspension medium with a structure sim-ilar to that of PDMS but that was curable at room temperature.

In the experiment with PDMS as the medium, uy CB waspoured into a PDMS matrix in a high-shear ball miller. The volumefraction of the CB aggregates in the suspension ranged from 1% to4.5% and each sample was sheared within 36 h for perfect dis-persion. An optical microscope (Nikon AFX-DX) was employed toobserve particle distribution following dispersion. Transmissionmicrographs were obtained using a mounted camera. A tinyamount of suspension (45 ll) was dropped onto a glass slide andphoyographs of random locations were taken. The viscosity wasmeasured in a DV-III cone and plate rheometer (Brookeld) forlow viscosity blends (1105 cp), and in a SR-5 parallel plate rhe-ometer for high viscosity blends (>104 cp). The electric conduc-tivity was measured using a RT-1000 multimeter (Marlborough),on a cell with two inserted, 110.05 cm3 metal electrodes, sepa-rated by 3 cm.

In the experiments with CB epoxy composite, DER-331 (Di-glycidyl ether of bisphenol A; Dow Chemical) combined withcuring agent HN-2200 (cycloaliphatic anhydride, Hitachi) wereused as a suspending medium. The uy CB was separately dis-persed into DER-331 and HN-2200 matrices, following the millingprocedure mentioned above. The well-dispersed samples weremixed in the ratio 5:4 (DER-331: HN-2200) and the rheology testto monitor curing and the conductivity test following post-curewere then performed. The morphology of the CB-lled compositeswas examined by optical microscopy mentioned above. Thin sec-tions (1 lm) were prepared using a MT 990 microtome (RMC).

Results and discussion

Figure 1 illustrates the dependence of the electric con-ductivity, in (W-cm)1, on the volume fraction of CBpowders for various PDMS viscosities. Figure 1 revealsthat, for a low viscosity PDMS (10 cp), the conductivityincreases sharply with CB loading. The conductivitythen becomes saturated at conductivity around 104 andchanges insignicantly when the CB loading is furtherincreased. Figure 1 reveals two notable phenomena.First, the saturation points increase with the viscosityof PDMS, contradicting the prediction of percolation

Fig. 1 Dependence of the electrical conductivity on the volumefraction of carbon black dispersed in PDMS liquids with variousviscosities. Diamonds on solid line 10 cp, triangles 100 cp, diamondson dotted line 500 cp, crosses 1000 cp, asterix 60 000 cp, circlessilicon rubber

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theory in which a xed 3-D array is assumed and con-ductivity is thus independent of the viscosity. Secondly,although a high viscosity liquid was applied- 60 000 cpPDMS, similar to a real polymeric molten stage, thesaturation point only increased to approximately 3%,which is far below that of a typical pelletized CB loading(generally 15%). The discrepancy is discussed in detaillater.

Close observation of the CB aggregate distributionreveals an interesting phenomenon. Figures 2a and b area series of photographs to illustrate the CB aggregatedistribution. Figure 2a shows that, at low PDMS vis-cosity (500 cp), the CB aggregates diuse and formloosely structured agglomerates. The increase in CBloading enlarges the agglomerates and, eventually, aconducting network is constructed. The conductivityincreases abruptly once this network is formed (fromFig. 2a.2 to a.3); the CB threshold loading can thus bedetermined. However, for a highly viscous PDMS (60000 cp), the aggregate diusion slows down signicantlyand the structured agglomerates are no longer formed.

The conducting network depends on the connection ofeach individual aggregate. Figure 2b displays a sequenceof pictures that demonstrate evenly distributed uyCB. The light transmission decreases as the CB loadingincreases. The aggregate-network can hardly be recog-nized since the CB aggregate is too tiny to be distin-guished individually under the optical microscope.However, the threshold value can still be determinedfrom the abrupt increase in conductivity (Fig. 2b.2 tob.3). Notably, the denition of threshold loading hereinis the CB loading that increases the conductivity up to104 (W-cm)1 magnitude.

Percolation was developed in 1970 to describe thelattice distribution in a matrix. The percolation thresh-old is the concentration at which an innite networkappears in an innite lattice. The observations presentedhere can be interestingly compared to the theoreticalresults. For a simple cubic lattice, the percolationthreshold is around 31%. However, for a hypercubiclattice for which d equals 7, the threshold value is only8.3% [19]. This result indicates that a more complexlattice geometry supports a smaller percolation thresh-old. Our experimental work gives a CB threshold ofabout or below 3%. This result is close to the empiricalpercolation threshold, 6%, provided by Rejon et al. [20].Since the CB dispersion lattice consists of either struc-tured aggregates or complex agglomerates, both arebelieved to form a network much easily and result in asmaller threshold than does any simple geometry lattice.In short, although the geometry of the CB particles istoo complex to be predicted by percolation theory, thetrend predicted by that theory ts the observation pre-sented here.

Figure 3 shows the dependence of relative viscosity(RV) on CB loading. Adding rigid particles to a liquidalters the ow eld. This hydrodynamic disturbance,rst theoretically described by Einstein, leads to an

Fig. 2a, b Optical micrographs for carbon black aggregatesdispersed in PDMS liquids. Dispersion of 0.13%, 0.27%, and0.54% carbon black by volume into 500 cp PDMS are shown in a.1to a.3. The correspondent conductivities are 6.361010, 1.50108,and 9.04106 (W-cm)1, respectively. In contrast, dispersion of0.81%, 1.09%, and 1.64% carbon black by volume into 60 000 cpPDMS are shown in b.1 to b.3. The correspondent conductivitiesare 3.561010, 5.63108, and 4.21106 (W-cm)1, respectively

Fig. 3 Dependence of relative viscosity (RV) on the volumefraction of carbon black dispersed in PDMS liquids with variousviscosities. Squares 10 cp, triangles 100 cp, crosses 500 cp, circles1000 cp, asterix 60 000 cp

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increase in viscosity because of the cutting of the owpattern and the rotation of particle. At very low con-centrations, the relative viscosity is linearly proportionalto the particle loading. The coecient of proportionalitydepends on the shape of the particle. For example,Einstein predicted that the coecient should be 2.5 forspherical particles. R. Simha and others have general-ized Einsteins work for particles with other shapes [21].Some experimental work has also been performed toexamine the viscosity behaviors due to the dispersion oftobacco virus particles or other asymmetric particles. Allstudies show that the asymmetry of the particle mark-edly increases the coecient of proportionality. Restat-ed, the coecient greatly exceeds 2.5 for a dilutedispersion of asymmetric particles. Figure 3 reveals thatfor suspensions of CB aggregates, each curve in its diluteregion is linear and its slope increases as the viscositydecreases. Figure 4 explains this nding. The gureclearly shows that huge agglomerates composed of CBaggregates can be easily formed at viscosity below1000 cp. The probability of collision followed by ag-glomeration is increased by the fast diusion of uyCB induced by a low viscosity liquid. In contrast, CBdiusion is suppressed as the viscosity of matrix in-creases and the CB agglomerates shrink to yield even-tually the aggregate dispersion shown in Fig. 4f. A

larger CB agglomerate is more complex and asymmetric,therefore, increasing the coecient of the RV propor-tionality in the dilute region (see Fig. 3).

Neither the Einstein nor the Simha theory can eec-tively describe high-concentration dispersion. At highconcentrations, viscosity can be increased by more thanan order of magnitude when the particle interactionbecomes extreme. Unfortunately, theories for such ma-terials are less developed and can be extremely complex.The sharp increase of RV is generally considered tofollow from the interaction between particles. However,the average distance between two CB agglomerates,which begin to interact with each other, is similar to theaverage distance between which an electron can be easilytransferred. Both distances are believed to be in the or-der of a nanometer. Accordingly, the deviation point ofRV under CB loading must be similar to the thresholdvalue of electric conductivity under CB loading. Figure 5shows the dependence of the RV deviation point and thethreshold conductivity on PDMS viscosity. As expected,these two curves match very closely. This result veriedthe above hypothesis that an agglomerate-network or anaggregate-network is formed; that is, the interactionamong particles starts to become important when thethreshold value of CB loading is reached.

Notably, the two mechanisms, previously discussed inrelation to Figs. 2a and b- the agglomerate-network andaggregate-network-can be clearly distinguished at thethreshold value of 1000 cp, as shown in Fig. 5. Thestructured agglomerate-network caused by particle dif-fusion dominates conductivity in liquids with a viscosityunder 1000 cp. The aggregate-network, however, domi-nates conductivity in liquids with a viscosity over1000 cp. This result is consistent with Fig. 4. In practice,a typical compounding process from 104 cp to 106 cpis far above 1000 cp. Therefore, the conductivitymechanism for a real polymer compounding is highly

Fig. 4af Optical micrographs for 0.43% volume fraction ofcarbon black dispersed in PDMS liquids with various viscosi-ties: (a) 10 cp (b) 100 cp (c) 500 cp (d) 1000 cp (e) 10 000 cp(f) 60 000 cp

Fig. 5 Dependence of the RV deviation point and thresholdconductivity on PDMS viscosity. Triangles CB conductivitythreshold, circles RV deviation point

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associated with the aggregate-network model. En-suring a perfect aggregate dispersion in a polymermatrix thus becomes very important. However, the bulkdensity of CB aggregate is known to be one twelfth ofthat of a typical polymer pellet. This extremely low ratiomakes the direct compounding of CB aggregate impos-sible. Compounding with pelletized CB, which has muchhigher bulk density than CB aggregate, has thus becomevery popular. Consequently, todays polymer industry isfocussed on shearing the pelletized CB into CB aggre-gates by extensive mixing. In practice, a realistic loadingof CB powders is about 15% [22, 23, 24], far beyond thesaturation point of 3% seen in Fig. 1. This result impliesthat most of the pelletized CB dispersed in a polymermatrix is not in the aggregate form. Either the pelletizingformulation or the compounding process must be im-proved to achieve an eective dispersion of CB aggre-gate [25, 26, 27].

An experiment involving silicon rubber, which has astructure similar to that of PDMS but a viscosity thatvaried in time, was performed to further investigate theimpact of viscosity on electric conductivity. The con-ductivity was monitored as the curing progressed (seeFig. 6). The conductivity remained at the initial valueindependently of the increase of viscosity. This resultsuggests that once the agglomerate network is estab-lished in the low-viscosity suspension, the increase of theviscosity due to curing only functioned to embed thestructure. Accordingly, the lowest viscosity in the curingprocess governs the conductivity of a CB thermosetsystem.

Fluy CB was dispersed in an epoxy system followingtwo curing processes- high temperature and room tem-perature- to further conrm the thermoset eect [28, 29].In high-temperature curing, the viscosity dropped rstbecause of the temperature eect [30]. It then rosedramatically due to fast crosslinking. In contrast, inroom-temperature curing, the viscosity slowly increasedbecause of light crosslinking. The viscosity then rose

sharply as the temperature nally rose to 50 C (seeFig. 7). Notably, the drop in viscosity was not observedfor the sample precured at room temperature. Figure 8shows that curing at high temperature yields higherconductivity than does curing at room temperature.Figure 9 displays the microtone of both systems andclearly shows that the high temperature sample possessesa superior structured agglomerate-network. Figures 8and 9 show that better conductivity follows the fall inviscosity that induces the formation of superior network.Again, the epoxy results conrm the above claim thatthe minimum viscosity in the curing process governs theconductivity of a CB thermoset system.

Conclusion

In this study, carbon black (CB) aggregates were dis-persed into various polymeric matrices. The eect ofmatrix viscosity on CB morphology, and thus on the

Fig. 6 Conductivity was monitored as the curing of silicon rubberprogressed

Fig. 7 Fluy carbon black dispersed in an epoxy system followingtwo curing processes. Triangles high temperature (90 C cure);circles low temperature (25 C precure, then 50 C cure)

Fig. 8 Dependence of electrical conductivity on the volumefraction of carbon black dispersed in epoxy matrices via dierentcuring processes. Triangles high-temperature curing; diamonds low-temperature curing

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composite conductivity, was comprehensively examined.The results yield the following conclusions:

1. Electric conductivity increases from 109 to 104 whenless than 3% CB aggregates were dispersed into thePDMS liquids of various viscosities. The CB thresh-old loading was found to rise from 1% to 3% as theviscosity increased from10 cp to 60 000 cp. Thisnding shows that an ideal loading with CB aggre-gates is far below that (generally 15%) of a typicalpelletized CB loading.

2. The microscope and the RV tests reveal that CB ag-gregates diuse and form an agglomerate-networkwhen the conductivity threshold is reached in a low-viscosity matrix. However, a CB aggregate-networkwas observed when the threshold value was reachedin a high-viscosity matrix. These two mechanismscould be distinguished at about 1000 cp.

3. When the CB aggregates have dispersed in a ther-moset matrix, the increase in viscosity during curingdoes not inuence the conductivity of the composite.The lowest viscosity in the curing process, however,was critical for CB dispersion morphology and,consequently, for ultimate electric conductivity.

Acknowledgement The authors would like to thank the NationalScience Council of the Republic of China for nancially supportingthis research under Contract No. NSC 892216-E-027013.

Fig. 9a, b Optical microscopy micrographs of 0.66% volumefraction of carbon black dispersed in epoxy matrices via (a) hightemperature curing (b) low temperature curing as described inFig. 7. The yielding conductivities for (a) and (b) are 1.67105 and3.65106 (W-cm)1, respectively

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